已知cos(a-π/6)=12/13且π/6<a<π/2,求tana
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已知cos(a-π/6)=12/13且π/6<a<π/2,求tana
π/6<a<π/2
0<a-π/6<π/3
sin(a-π/6)=5/13
sina=sin(a-π/6+π/6)=sin(a-π/6)cos(π/6)+cos(a-π/6)sin(π/6)
=(12+5*3^(1/2))/26
cosa=cos(a-π/6+π/6)=cos(a-π/6)cos(π/6)-sin(a-π/6)sin(π/6)
=(12*3^(1/2)-5)/26
tana=sina/cosa=(12+5*3^(1/2))/(12*3^(1/2)-5)
0<a-π/6<π/3
sin(a-π/6)=5/13
sina=sin(a-π/6+π/6)=sin(a-π/6)cos(π/6)+cos(a-π/6)sin(π/6)
=(12+5*3^(1/2))/26
cosa=cos(a-π/6+π/6)=cos(a-π/6)cos(π/6)-sin(a-π/6)sin(π/6)
=(12*3^(1/2)-5)/26
tana=sina/cosa=(12+5*3^(1/2))/(12*3^(1/2)-5)
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